1. Field of the Invention
The present invention relates to a variable reluctance (VR) resolver, and in particular to a VR resolver which has a rotor which is shaped such that the gap permeance varies according to the sine of the rotational angle, which is expressed by the mechanical angle φ or the electrical angle θ corrected by a shaft angle multiplier (shaft angle multiplication factor).
2. Related Art
In the past, the shape of a rotor in a VR resolver was formed as described below in (1)–(3).
(1) In the case of a VR resolver whose rotor has no winding and which utilizes variations in reluctance at a gap, when the rotor is shaped to have a property such that the gap permeance varies in accordance with the sine of the rotational angle (referred to below as a “sinusoidally varying property”), the rotor has a simple structure of an iron core without windings, and a sinusoidal voltage with a period corresponding to the shape of the salient poles of the rotor is output by the output windings. When the inner periphery of the stator is a perfect circle, the length re between the outer periphery and the center of the rotor at an angle θ is determined by the following Equation 1.
                              r          θ                =                              r            1                    -                                    δ              0                                      1              +                                                (                                                                                    δ                        0                                                                    δ                        1                                                              -                    1                                    )                                ⁢                cos                ⁢                                                                  ⁢                n                ⁢                                                                  ⁢                θ                                                                        Eq        .                                  ⁢        1            Here,
r1 is the radius of the inner periphery of the stator,
δ0 is the gap between the stator and the rotor at 90° and 270°,
δ1 is the gap between the stator and the rotor at 0°, and
n is the shaft angle multiplier.
The angular error of a 4× resolver fabricated on the basis of the above Equation 1 and having a stator inner diameter of 46.4 mm is shown as the conventional example in the following Table 1 and in FIG. 2B. Table 1 shows the angular error sampled every 30°.
FIGS. 2A and 2B are graphs showing the measured angular error of a VR resolver with a shaft angle multiplier of 4× according to an embodiment of the present invention, and that of a conventional VR resolver with a shaft angle multiplier of 4×. FIG. 2B is a graph of the measured angular error of a conventional VR resolver with a shaft angle multiplier of 4× and a stator inner diameter of 46.4 mm.
Here, the “angular error” means the difference between the mechanical angle when the resolver is made to rotate and the electrical angle of the resolver output signal resulting from the rotation. The angular error=mechanical angle−(electrical angle/shaft angle multiplier).
The “error” is expressed in minutes ( 1/60 of a degree).
If the shaft angle multiplier is 1×, then n=1 in Equation 1, and the rotor becomes heart shaped.
A controller (not shown) comprising a microcomputer is employed in order to measure the angular error. At the time of measurement, the controller fetches the output signal of a sensor which senses the mechanical rotational angle of the rotor, the output signal of the output winding of the stator, and the like; performs necessary calculations; and determines at least the angular error at every angle and outputs the error.
In the following Table 1, “This invention” indicates the angular error properties of a below-described embodiment of the present invention.
TABLE 1Angular Error (minutes)ConventionalPresentAngle (°)ExampleInvention0003013.8−1.560−3.1−390−1.8012013.8−1.5150−3.1−31800021013.8−1.5240−3.1−3270−1.5030013.8−1.5330−3.1−3360−4.60
As shown by the conventional example in the above Table 1, the angular error for a conventional rotor, i.e., the angular error of a conventional VR resolver [=mechanical shaft angle (mechanical angle φ)−electrical shaft angle (electrical angle θ/shaft angle multiplier N)] is large, and at an angle of 30°, 120°, 210°, and 300°, a large error 13.8 minutes occurs.
(2) A conventional VR resolver was constructed as described above, so it had the following problems. Equation 1 is based on a model which assumes that magnetic flux passes in a straight line in the gap towards the center of the rotor, so it does not describe an actual rotor. Namely, in regions where the gap width is large and there are large variations in the magnetic field, the magnetic flux is curved, so a leakage flux is formed at, for example, the end surfaces of the salient poles of the rotor. Therefore, a harmonic error component other than a first order error component, and typically a third order error component, is added to the output signal corresponding to the angle of the resolver.
In light of this problem, in the past, the following Equation 2 has been proposed to remove this error component.
                              δ          θ                =                                            δ              0                                      1              +                                                (                                                                                    δ                        0                                                                    δ                        1                                                              -                    1                                    )                                ⁢                cos                ⁢                                                                  ⁢                n                ⁢                                                                  ⁢                θ                                              +                      K            ⁡                          (                              1                -                                  cos                  ⁢                                                                          ⁢                  2                  ⁢                                                                          ⁢                  θ                                            )                                                          Eq        .                                  ⁢        2            Here,
δθis the gap between the stator and the rotor at a rotational angle θ,
δ0 is the gap between the stator and the rotor at 90° and 270°,
δ1 is the gap between the stator and the rotor at 0°,
n is the shaft angle multiplier, and
K is a constant.
Equation 2 is Equation 1 to which the correction term K(1−cos 2θ) has been added. Namely, a simulation is carried out such that an output signal which includes an error component, which is the difference between an actually measured output voltage and a theoretical value, becomes a signal including a corrected signal which corrects the error component and a reversed error component which is the error component with its sign reversed, and the value of K in the correction term is determined. The value of the constant K varies in accordance with the correction amount in the simulation.
In this case, the error component has its sign reversed and then it is added to the measured value, so the error component is corrected (see, for example, Patent Document 1).
(3) When the induced voltage in the output windings is not a pure sine wave but includes a harmonic component, there are cases in which the following Equation 3 is used to define the shape of salient poles which minimize these harmonic components.
                              R                      θ            ⁢                                                  ⁢            2                          =                              R            1                    -                                    k              ⁢                                                          ⁢                              δ                1                                                    1              +                                                (                                      k                    -                    1                                    )                                ⁢                                  cos                  ⁡                                      (                                          N                      ⁢                                                                                          ⁢                                              θ                        2                                                              )                                                                                                          Eq        .                                  ⁢        3            Here,
Rθ2 is the distance between the outer periphery and the center of the rotor core at a spatial angle θ2,
R1 is the inner radius of the stator core,
δ1 is the minimum gap length, and
N is the number of salient poles on the core.
In this example, the rotor shape is selected such that when the center of a salient pole serves as the origin and the spatial angle which indicates the position on the outer periphery of the rotor is represented by θ2, the variation in the gap permeance by the salient poles is cos(Nθ2) (see, for example, Patent Documents 2 and 3).
Patent Document 1: Japanese Patent Application Laid-Open (kokai) No. Hei 11-118416.
Patent Document 2: Japanese Patent Application Laid-Open (kokai) No. Hei 11-313470.
Patent Document 3: Japanese Patent Application Laid-Open (kokai) No. 2000-105133.
Various conceivable parameters, such as the number of salient poles, stator windings, or curved flux which excludes flux extending in a straight line in the radial direction in a gap, can be used to correct the gap permeance, which is the inverse of the gap between the stator and the rotor, so as to vary sinusoidally.
In the conventional method of correction described above as example (2) of the background art in which the error component is reversed in sign and added to the measured value, the reason why K(1−cos 2θ) is added as a correction term is not disclosed and is unclear, and only correction which varies with two times the rotational angle θ is at all possible. Furthermore, the value of the constant K in the correction term varies in accordance with the amount of correction in a simulation, and as a result, there is no great difference from the conventional correction method in which correction is carried out by simulation.
In light of these circumstances, the conventional methods can not be said to properly cancel harmonic components other than a first order component, and typically a third order harmonic error component, contained in the output signal.
Above-described example (3) of the background art forms the shape of the salient poles in accordance with above-described Equation 3, but the effect of harmonics still remains, and problems remain with respect to its practical application.